Which of the following numbers is a multiple of 5? ${41,51,69,85,99}$
The multiples of $5$ are $5$ $10$ $15$ $20$ ..... In general, any number that leaves no remainder when divided by $5$ is considered a multiple of $5$ We can start by dividing each of our answer choices by $5$ $41 \div 5 = 8\text{ R }1$ $51 \div 5 = 10\text{ R }1$ $69 \div 5 = 13\text{ R }4$ $85 \div 5 = 17$ $99 \div 5 = 19\text{ R }4$ The only answer choice that leaves no remainder after the division is $85$ $ 17$ $5$ $85$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $5$ are contained within the prime factors of $85$ $85 = 5\times17 5 = 5$ Therefore the only multiple of $5$ out of our choices is $85$. We can say that $85$ is divisible by $5$.